Resonant vibratory apparatus



Sept. 10, 1968 D. ENSMINGER 3,400,892

RESONANT V i BRATORY APPARATUS Filed Dec. 2, 1965 FIG. 2

IN VEN TOR. DALE ENSMINGER BY GRAY, MASE & DUNSON ATTORNEYS WWZWW UnitedStates Patent 3,400,892 RESONANT VIBRATORY APPARATUS Dale Ensminger,Columbus, Ohio, assignor to The Battelle Development Corporation,Columbus, Ohio, a corporation of Delaware Filed Dec. 2, 1965, Ser. No.531,319 2 Claims. (Cl. 239-102) ABSTRACT OF THE DISCLOSURE A full-Waveresonant ultrasonic horn atomizer comprising, from the left: aquarter-wave section 17, two electronically driven, clampedpiezoelectric disks 11, 12, and a half-wave section 19, all of fulldiameter; a quarterwave section of reduced diameter for mechanicalamplification; and a flange 22, supplied with liquid, at thedisplacement antinode 25, and tuned to flex resonantly at the operatingfrequency.

This invention relates to vibratory apparatus, and particularly toresonant vibratory apparatus having a displacement antinode at an endthereof.

In a typical form of the present invention, resonant vibratory apparatushaving a displacement antinode at an end thereof comprises means forsupplying liquid to said end, and a resonantly flexible flange at saidend. The flange preferably extends outwardly from the end in a planesubstantially perpendicular to the direction of vibration of said end.

In a preferred embodiment of the apparatus, the flange comprises a diskof thickness t extending a radial distance I outwardly beyond said end,t and l in inches being chosen substantially in accordance with f is theresonant frequency of said apparatus in c.p.s.,

p the density of the flange material in pounds per cubic inch,

g is the acceleration of gravity, 386 in./sec. and

E is Youngs modulus of elasticity of the flange material in p.s.i.

where When the apparatus is used for atomizing, the liquidsupplyingmeans furnishes liquid to the face of the flange and the resonantvibration of the flange causes the fluid to spread over the face andbecome atomized from substantially the entire area thereof.

An important advantage of this invention is exemplified by thesubstantially increased capacity that it has provided in apparatus suchas ultrasonic atomizers as used in miniaturized burners forthermoelectric generators and other military equipment. Conventionalultrasonic atomizers, which may be similar to the atomizer shown in FIG.'1 but without the flange 22, when miniaturized, lose a substantialproportion of their capacities for atomizing fluid. In the presentinvention, however, the thin resonantly flexible flange increases theeffective atomizing area without the usual accompanying loss ofdisplacement that is experienced with flanges and other end pieces thatare not tuned to match the resonant frequency of the driving transduceror are not flexible. Miniature atomizers according to the presentinvention have more than three times the capacity obtainable withcomparable atomizers of known conventional designs, with no accompanyingdisadvantages.

The increase in capacity is not limited to small atomizers. Similarincreases of efficiency are realized .re-

ice

gardless of the size, where the same basic principles of resonance inthe flange are incorporated in the design. Thus at any size the rate ofatomization can be increased by a substantial factor over thatobtainedwith conventional units using such acoustic transformers asstraight stepped horns. The increase in capacity is attributable partlyto the better distribution of the film of liquid across the atomizingsurfaces. The distribution of the ultrasonic or sonic stresses acrossthe face of the resonant flange is such that the fluid is drawn out soas to spread across substantially the entire front surface of the flangeand become atomized therefrom. Another factor that contributes to theincreased capacity is the enlargement of the area over which theeffective atomizing forces operate. The effective atomozing forces of aconventional atomizer are condensed about the center (axis) of the horn.In the present invention the effective atomizing forces of the flangeextend nearly to the periphery of the flange.

In the drawings:

FIG. 1 is a simplified sectional view of typical resonant vibratoryapparatus according to this invention.

FIG. 2 is a graph in rectangular coordinates aligned with FIG. 1 andshowing displacement as a function of location along the length of theapparatus of FIG. 1.

In typical ultrasonic atomizers according to this invention, atomizationoccurs as the result of vibrating a thin film of fuel. The fuel isflowed over the surface of a transducer vibrating at a frequency in theneighborhood of kc. The vibration causes a wave pattern in the fuel overthe entire surface area. With suflicient vibration amplitude, the wavesthrow ofl droplets from. their crests. The droplet size is a function ofthe atomizer vibration frequency, fuel density, viscosity, and surfacetension. The maximum fuel rate depends upon the atomizing area, thefrequency and amplitude of vibration, and the uni formity of fueldistribution over the atomization area. The vibrating surface of theatomizer is the end of a small aluminum cylinder that is part of theatomizer; and fuel is supplied to the face of the cylinder through asmall axial hole. The atomizer is driven by an electronic driver, whichconverts 12 v. direct current to highvoltage, 85 kc. alternating currentneeded to operate the transducer.

FIG. 1 shows a preferred form of such an ultrasonic atomizer. The activeelements of the atomizer 10 are two piezoelectric disks 11, 12 ofle'ad-zirconate-titanite material (such as Clevite PZT-4, a product ofPiezoelectric Division, Clevite Corporation, Bedford, Ohio), whichexpand and contract in a thickness mode at the frequency of the drivingvoltage from a driver 13 placed across the faces of each disk. The disks11, 12 are clamped between flanges 14, 15 with a foil 16 of copperbetween them to serve as a center electrode, and with the flanges 14, 15serving as the outer electrodes. The center electrode 16 is at highvoltage, and the outer electrodes 14, 15 are near ground potential,although they are electrically isolated from ground.

The clamping flanges 14, 15 are parts of two aluminum horns 17, 18which, with the piezoelectric disks 11, 12, form a full-wave resonantvibrator. The electronic driver 13 must provide power at the resonantfrequency of the assembly; if this frequency changes slightly withtemperature and fuel flow, the driver frequency must also change inorder to maintain resonance. This it does. A preferred form of suchdriver is disclosed in United States patent application Ser. No.513,171, filed Dec. 13, 1965, of Harvey H. Hunter, for ElectronicOscillators.

The horn 17 to the left of the flange 14 in FIG. 1 is a quarter-wavestructure. The atomizing horn 18, to the right of the flange 15,includes a half-wave section 19 at full diameter, plus a quarter-wavesection 20 of reduced diameter. The elfect of the reduction ofcross-section is an increase in amplitude of longitudinal vibration,inversely proportional to the cross-sectional area. The step shown at 21provides a mechanical amplification of eight. The flange 22 at the tipof the atomizer is tuned to flex at the operating frequency of theatomizer so that the amplification factor is maintained. The flange 22serves to add atomization area at the tip and thus increase atomizercapacity.

FIG. 1 includes symbols used in the design equations. The relation ofvibrational amplitude, or displacement, to axial position on theatomizer 10 is shown in FIG. 2, which is aligned with FIG. 1.

The atomizer 10 can be considered as an acoustic transmission line. Thetransverse dimensions are small compared to a wavelength and, therefore,the structure simulates a thin bar. The general equation for theacoustic impedance of a thin bar-type transmission line of uniformcross-section is z: j( c)A tan L where The atomizer 10 is actually aseries of short transmission lines joined at points where the acousticimpedances of the mating lines are matched at resonance. In the designstage, the matching is accomplished by applying the appropriate vlaues,which have been predetermined by the design objectives in Equation 1 foreach of the mating segments, thus obtaining simultaneous equations thatcan be solved for the unknown dimensions. For example, in FIG. 1, thecomponents are two 0.5-inch diameter X 0.10-inch thicklead-zirconate-titanate piezoelectric disks 11, 12 sandwiched betweenaluminum transmission lines 17, 18. The equivalent length of theassembly is one Wavelength at 100 kc., with velocity nodes located atthe interface 16 between the two ceramic disks 11, 12 and at the step 21near the feed tube 23. The diameter of the dummy horn 17 and of thelarger section 19 of the active horn 18, which is selected to be equalto that of the ceramic disks 11, 12, is 0.5 inch. Other arbitrarilychosen dimensions are:

Inch Smaller diameter of active horn 0.180 Bolt-flange diameter 1.0Bolt-flange thickness 0.135

The flange 22 at the atomizing tip is matched to the horn 18, so thatthe dimension identified as M2 is the same as though the flange were notpresent. Since this dimension includes two quarter-wave segments, itsvalue can be determined by the familiar formula c=hf Aquarter-wavelength in aluminum at 100 kc. is approximately 0.503 inchand M2 is 1.005 inch. The remaining horn dimension to be calculated isthe length a. This is done by determining the impedance at x=a and atx=b, designated as Z1 and Z2, respectively. The equations are:

1= 1'( )..1A2 an f ne-0.135

Where B would be the length of b if the horn were of uniform diameter.The subscripts c and al refer to the piezoelectric disks and thealuminum, respectively. By introducing the known values into Equation 3and by using the relationship (pC) /(pC) :,2.15, the calculateddimension a=0.359 inch.

The atomizer 10, excluding the section identified by the dimensionalnotation M2, is acoustically symmetrical about the plane 16 thatcontains the two mating faces of the piezoelectric disks 11, 12; Thus,all of the required dimensions, except those of the flange 22 at theatomizing tip, are now known.

The small flange 22 at the atomizing tip is designed to flex at theresonant frequency of the assembly. The fiexural frequency is givenapproximately by for aluminum, where or, rearranging,

g: racer/VF;

In the previous example, at f=100 kc.,

The dimension 1 is chosen arbitrarily to increase tip area. With achoice of 1:005 inch, t=0.024 inch.

The constant 0.537 includes the density of aluminum, so Equation 4applies only to aluminum flanges. It can be generalized to gE -6f gEwhere p is the density of the flange material in pounds per cubic inch.

The thin copper electrode 16 between the ceramic disks 11, 12 is assumedto be small enough that it can be neglected with little error in thecalculation.

The atomizer 10 of the example above had several resonant frequencies,including one at 100 kc. However, the combination of the atomizer andthe final driver performed best at kc., and was used at that frequencyin a burner. The flexing flange 22 at the atomizer tip was subsequentlytuned for 85 kc.

Although the ultrasonic atomizer 10 appears simple, all parts are highlystressed, and must be made and assembled with care to assure properoperation and satisfactory life. In making the aluminum horns 17, 18, itis extremely important that dimensions be held within :0.001 inch, andthat the finish be free of tool marks and scratches. Any scratches willact as stress raisers and initiate premature fatigue failure. The activehorn 18 should be fully polished, and particular care should be takenwith flange fillets.

To insure maximum sensitivity, power transfer, and useful life of'thetwo piezoelectric elements 11, 12 used in the atomizer- 10, it isnecessarythat a compressive force be applied to them. With no couplingagents between the parts of the atomizer, the clamping pressure shouldbe about 13,000 p.s.i. This pressure is obtained by applying a torque of10.4 in.-lb. to the six bolts 24 used to 5 assemble the atomizer. Inorder to avoid damaging the brittle piezoelectric disks 11, 12, thebolts 24 are first installed finger-tight, and then pairs ofdiametrically opposed bolts 24 are tightened by small increments, onepair at a time, until the full torque is applied.

Fuel is supplied to the active tip 25 of the atomizer 10 through asmall, axial hole 26 extending to meet a radial hole 27 in the largesection 19 of the atomizer 10, as close to the step 21 as possible. A0.032-in.-O-D hypodermic tube 23, attached by press-fitting into theradial hole 27, supplies fuel to the atomizer 10. The step 21 is locatedat a node with zero displacement, providing a good attachment point bothfor fuel supply and for mounting of the atomizer 10, as in a burner.

Ideally the atomizer should be mounted at a vibration node. However, thenode is a plane that shifts as the frequency varies. Frequency shiftsoccur with changes in atomizer temperature and with changes in thicknessof the fuel layer on the atomizer tip. For this reason, any materialused for mounting purposes is subjected to some ultrasonic energy.Because of this, the mounting assembly causes a reaction on the assemblythat is reflected back into the electrical system. The mount nearlyalways constitutes a source of loss. Various methods have been tried tominimize the reaction of the mounting system. Perhaps the best mount,from an ultrasonic standpoint, has been two thin polytetrafluoroethylenewashers, through .which the atomizer was fitted. However, this mount isnot suitable for use in a burner. For mounting in a burner, the washerswere replaced by an aluminum mounting tube 28 containing six radialscrews 29 for clamping to the atomizer 10.

While the form of the invention herein disclosed constitutes a presentlypreferred embodiment, many others are possible. It is not intendedherein to mention all of the possible equivalent forms or ramificationsof the invention. It is to be understood that the terms used herein aremerely descriptive rather than limiting, and that various changes may bemade without departing from the spirit or scope of the invention.

What is claimed is:

1. Resonant vibratory apparatus having a displacement antinode at an endthereof, comprising means for supplying a liquid to said end, and aresonantly flexible flange at said end, wherein said flange comprises adisk of thickness t extending a radial distance I outwardly beyond saidend, t and l in inches being chosen substantially in accordance with trZ 1 6f gE where f is the resonant frequency of said apparatus in c.p.s.,

p is the density of the flange material in pounds per cubic inch,

g is the acceleration of gravity, 386 in./sec. and

E is Youngs modulus of elasticity of the flange material in p.s.i.

2. In resonant vibratory apparatus having a displacement antinode at anend thereof and means for supplying a liquid to said end, theimprovement the comprises providing a resonantly flexible flange at saidend, wherein said flange comprises a disk of thickness t extending aradial distance I outwardly beyond said end, t and l in inches beingchosen substantially in accordance with l P t2-6f gE where f is theresonant frequency of said apparatus in c.p.s. p is the density of theflange material in pounds per cubic inch, g is the acceleration ofgravity, 386 i-n./sec. and

E is Youngs modulus of elasticity of the flange material in p.s.i.

References Cited UNITED STATES PATENTS 2,895,061 5/1959 Probus 2391022,949,900 8/1960 Bodine 239-102 3,110,825 11/1963 Miller 239-1023,114,654 12/ 1963 Nishiyama et al 239102 EVERETT W. K-IRBY, PrimaryExaminer.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No.3,400,892 September 10, 1968 Dale Ensminger It is certified that errorappears in the above identified patent and that said Letters Patent arehereby corrected as shown below:

Column 1, lines 37 to 39, the formula should appear as shown below:

Column 3, lines 73 to 75, the left-hand portion of the formula reading:

s should read z Column 6, lines 24 to 27, the formula should appear asshown below: i

Signed and sealed this 3rd day of February 1970.

(SEAL) Attest:

EDWARD M.FLETCHER,JR. WILLIAM E. SCHUYLER, JR

Attesting Officer Commissioner of Patents

